# n203 — The bare-gradient bargain: c_g = c costs one parameter, and the statics barely notice


**CORRECTION (n215, 2026-07-11):** the 9- and 13-complex rows of the bargain table were contaminated by the n202 Rust bug (cubic row clean). The corrected bargain is much more expensive: b*/S_shear ≈ 2.1 (9-derived) to 3.0 (axes-0.25) — the bare term must be 2–3× the induced stiffness, no longer a modest fraction. The proposal was already withdrawn (§35); the correction makes it worse and is recorded for completeness.

**Date:** 2026-07-11 · **Tool:** `cg-rust/` extended (the bargain table). **Reproduce:** `cd cg-rust && cargo run --release`. **Follows:** n202 (the mapped 15% deficit).

## The question

n202 closed the artifact hope: at leading induction order the blind shear channel is subluminal everywhere in the complex family (max c_g²/c² ≈ 0.85). The only local repair the Action's structure admits is a **bare gradient term** b·(∇δk)² in the elasticity — postulate 3 made the bare elasticity local, but locality was minimality, not a derivation. If b exists, c_g²(b) = (S_induced + b)/I is linear in b, and GW170817 (|c_g/c − 1| ≲ 10⁻¹⁵) *pins* b — the same move that pinned R = 1 (clusters) and the edge weights (isotropy). The question with teeth: **what does that b do to everything else?** An isotropic bare gradient term feeds every k-channel — including the watched trace sector that delivers Newton and Coulomb.

## The computation

For each complex: the shear channel's induced stiffness S_sh and inertia I (exact two-phonon sums); b* = c²·I − S_sh (the GW demand); and the same b* measured against the *trace* channel's induced stiffness S_tr (the statics' scale).

| complex | b*/S_shear | **b*/S_trace** |
|---|---|---|
| 3D cubic | 0.95 | 0.048 |
| 9-complex, uniform | 0.44 | 0.006 |
| 9-complex, derived weights | 0.23 | 0.003 |
| 9-complex, axes 0.25 (family max) | **0.18** | **0.002** |
| 13-complex A / B | 1.5 / 1.9 | 0.021 / 0.026 |

## The finding

**The watched sector's induced stiffness is ~100× the blind sector's** — because the monitor's dressing pours stiffness into what it watches and none into what it cannot see. Consequence: the bare term the shear channel needs to reach the light cone is a **0.2–0.6% perturbation to the sector that delivers Newton and Coulomb** (9-complex family; even the cubic pays only 4.8%). The statics absorb it into the G calibration and the Coulomb corrections appear only at the lattice scale. The bargain, priced: *one new bare parameter, pinned by independent data, whose side effects are at the 10⁻³ level.*

Second face: b*/S_sh itself selects the complex — the 9-family needs a modest fraction (0.18–0.44) while the 13-complexes need *more bare than induced* (1.5–1.9, structurally ugly). Cheapness and the n202 maximum point at the same family.

## What this is, honestly

A **proposed amendment to postulate 3** (bare elasticity: local → local + gradient, one coefficient), not an adopted one: it converts condition B from a kill into a calibration, and that is exactly the kind of move the adversarial process exists to stress. Submitted to review before adoption. What it does *not* do: derive c_g = c (it inputs it — as G is input); explain why b takes that value (the microphysics owes it, as it owes u″); touch the inertia postulate (kinetic stays purely induced — the marginality/masslessness mechanism is untouched, since a q² term gaps nothing).

**Class: computation [A-model, exact sums]; the amendment [proposal — pending adversarial review]; the "cheapness" finding [A]: the 100× watched/blind stiffness asymmetry is the monitor's own signature.**